Chapter 6: Q 84E (page 589)

In the following exercises, factor each trinomial of the form $x^{2} + b x y + c y^{2}$
$r^{2} + 5 r s - 24 s^{2}$

Short Answer

Expert verified

The binomial factors of the equations are $(r + 7 s) (r - 4 s)$ .

Step by step solution

Step 1. Given information

The given equation is $r^{2} + 5 r s - 24 s^{2}$

Step 2. Writing factors as two binomial with first term r and second term s.

The factors should be written as two binomials with first term r and second term s.

$(r s) (r s)$

The product of the two numbers is 28,and their sum is 3. Because the third term sign is negative, the sum seems to be a difference.

$[\begin{matrix} Factors & 28 & 14 & 7 \\ 1 & 2 & 4 \\ Difference & 27 & 12 & 3 \end{matrix}]$

So form of binomial is $(r s) (r s)$ . $(r 7 s) (r 4 s)$

Step 3. Finding factors

The larger binomial second term is also positive because the second trinomial term is positive

Because the third trinomial term is negative, the binomial signs are transposed.

The binomial factors are as follows: $(r + 7 s) (r - 4 s)$

Step 4. Checking the factors

$Check : Multiply the factors . (r + 7 s) (r - 4 s) = r ² - 4 r s + 7 r s - 28 s ² [Multiply] = r ² + 3 r s - 28 s ² True [Group the like terms]$

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In the following exercises, factor each trinomial of the form $x^{2} + b x y + c y^{2}$
$r^{2} + 5 r s - 24 s^{2}$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Writing factors as two binomial with first term r and second term s.

Step 3. Finding factors

Step 4. Checking the factors

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In the following exercises, factor each trinomial of the form x2+bxy+cy2r2+5rs-24s2

Short Answer

Step by step solution

Step 1. Given information

Step 2. Writing factors as two binomial with first term r and second term s.

Step 3. Finding factors

Step 4. Checking the factors

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Probability and Statistics

Statistics

Pure Maths

Discrete Mathematics

Calculus

Study anywhere. Anytime. Across all devices.

In the following exercises, factor each trinomial of the form $x^{2} + b x y + c y^{2}$
$r^{2} + 5 r s - 24 s^{2}$